Other Math Answers

State the reason why least squares method canot be used in fitting exponential curve.

Given the three selected points X₁=55.8, X₂=138.6,X₃=250.8 and the corresponding times

t₁=2,t₂=20 and t₃=38, fit the exponential curve X_t=a+bc^t using the method of 3 selected points

Consider the linear additive model of the randomized block design . Derive the estimates for the treatment effects and for the block effects

State the statistical model for each of the following experimental designs and explain what each of the components in the model stand for

i)Completely randomized designs

ii)Randomized Block Design

iii)Latin Square Design

iv)Balanced Incomplete Design

Supposse that y₁,y₂,y₃,y₄ are four observations,write down a pair of linear functions of the four observations which are mutually orthogonal

in design and analysis of experiments define the orthoganality of two contrasts

An experimenter wishes to compare 6 treatments and has resources to take a total of 36 observations, 6 for each treatment. How many residual(error) degrees of freedom to compare treatments are there if she uses

1) A completely randomized design

2)A randomized complete block design

3) A latin square design

Consider a completely randomized randomized design experiment under the fixed effects linear additive model y_ij=μ+t_i+e_ij where μ is the general effect, t_i is the i^th treatment effect and e_ij ^,s are independently normally distributed random variables with common mean zero and variance σ²(i=1,2,......,k) and (j=1,2,.......,n_i). The objective of the experiment is to test the hypothesis H₀ :t₁=t₂=_ _ _=t_k against H₁: all t_i ^,s are not equal.

Obtain the least squares estimates of the effects μ and t_i ^,s and show that they are unbiased

with reference to experimental design briefly describe the following terms

1) Randomization

2)Replication

3)Blocking

Show that in a 2² experiment, the main effects and interaction are mutually pairwise orthogonal